After fixing the time drifting , the phase fluctuation is the target for the second stage, which is also larger than the fluctuations in lab, due to environment vibration. We measured a phase rate of 0.03 \(rad/\mu s\)  through field-deployed fiber, or equivalent to 17 degree in 10 \(\mu \) s, as shown in Fig REF (b). The phase reference pulse and the corresponding phase estimation method [1]}, [2]} are used to compensate for this phase drift in post-processing. We time-multiplex the quantum signal together with strong phase reference pulses using intensity modulator. The superconducting nanowire single photon detectors (SNSPD) used in our experiment has a 60 dB dynamic range, which can measure both the quantum signal and strong phase reference signal. According to the measurement result of phase reference signals, we can compensate the phase difference in postprocessing, and then the optical phase sensitive interference is achieved. (See supplementary for details of the experimental setup)
